Binomial Divisibility and Carry Conditions for Primitive Pythagorean Triples in the Context of Lattice Paths

This manuscript investigates an arithmetical and combinatorial property of primitive Pythagorean triples (a,b,c). We analyze the condition under which the product (a+b)c divides the binomial coefficient, which corresponds to the number of monotone lattice paths from (0,0) to (a, b). This document serves as the formal proof and mathematical foundation for the corresponding integer sequence submitted to the On-Line Encyclopedia of Integer Sequences (OEIS).

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-05
DOI
https://doi.org/10.5281/zenodo.23160514
Primary Topic
Advanced Combinatorial Mathematics
Type
preprint
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preprint

Binomial Divisibility and Carry Conditions for Primitive Pythagorean Triples in the Context of Lattice Paths

Pascal T. Grülling
Zenodo (CERN European Organization for Nuclear Research)
Advanced Combinatorial Mathematics
preprint

Binomial Divisibility and Carry Conditions for Primitive Pythagorean Triples in the Context of Lattice Paths

Pascal T. Grülling
preprint en

Abstract

This manuscript investigates an arithmetical and combinatorial property of primitive Pythagorean triples (a,b,c). We analyze the condition under which the product (a+b)c divides the binomial coefficient, which corresponds to the number of monotone lattice paths from (0,0) to (a, b). This document serves as the formal proof and mathematical foundation for the corresponding integer sequence submitted to the On-Line Encyclopedia of Integer Sequences (OEIS).

Zenodo (CERN European Organization for Nuclear Research)
Advanced Combinatorial Mathematics
DOIOpen Access PDFOpenAlex
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Binomial Divisibility and Carry Conditions for Primitive Pythagorean Triples in the Context of Lattice Paths — Pascal T. Grülling · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS